In the cervical region of the vertebral column, there is only a small amount of space available for receiving intervertebral prostheses. Even a slight shifting of prosthesis parts in the dorsal direction can affect the nerves of the spinal cord. Secure fixation of the prostheses is therefore of great importance. In the case of intervertebral prostheses for the lumbar region of the vertebral column, it is known for the cover plates of the prosthesis which face the adjacent vertebral bodies to be provided with ribs or projections which engage in prepared grooves in the vertebral bodies or are designed to be sharp and self-cutting. This is made possible by the fact that the vertebral bodies of the lumbar vertebral column are relatively large and high, so that there is enough space available for fixation devices of this kind. This also applies to fixation flanges which are provided at the ventral edge of the cover plates of the prostheses in order to receive bone screws for securing the cover plates on the associated vertebral bodies. The smallness and low height of the vertebral bodies in the cervical region often rules out the use of these fixation devices or means that said fixation devices appear unsatisfactory. This is all the more so given that ventrally protruding parts of the prostheses have to be avoided, because these can lead to irritation of the esophagus lying immediately in front of them.